Lec 3 Fatigue Failure 031004_for_students

8/6/2019 Lec 3 Fatigue Failure 031004_for_students

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Chapter 6 Fatigue Failure

Theories


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Fatigue Failure

Occurs when stresses are changing

throughout the life of a part.

_______________________ starts with a

crack that propagates until a catastrophic

failure occurs.

This usually begins at a manufacturing defector stress concentration that is subjected to

tensile stresses for part of its load cycle.


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Fatigue-Failure Models

Stress-Life - cyclic stresses are kept

below fatigue strength or endurancelimit. Most widely used.

Strain-Life - complicated not often used.

_________________ - sometimesused, gaining favor especially in the

aircraft and aerospace industry.


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Fati Str ss

s

-10000

-50000

5000

10000

15000

20000

25000

30000

0 2 4 6 8 10

adC

cl s

A

lidS

tr

ss

-

si

Wa

Wa

Wa

Wm

Wm

Full R

rs

d R

at d Fluctuati


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Fully Reversed Failure Criteria

Most data comes from . . Moore

rotating-beam test. Highly polished specimen of . inches

in diameter is subjected to pure bending

stresses that are alternated by rotating

the specimen.

otation is at 7 rpm.

Takes / day to reach 6 cycles.


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S-N Curve for Steel with Sut = 100 ksi

10000

100000

1.0E+3 10.0E+3 100.0E+3 1.0E+6 10.0E+6 100.0E+6

Cycles to Failure - N

Fatigue

Strength

-Sf


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Endurance Limit and FatigueStrength

Endurance Limit of a Material (Se) -

stress below which fatigue failure doesnot occur regardless of the number of

stress cycles.

____________________Strength of a

Material (Sf) -stress below which fatigue

failure does not occur for a specified

number of stress cycles.


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Typical S-N Curve for Non-Ferrous Metals

10000

100000

1.00E+03 1.00E+04 1.00E+05 1.00E+0 1.00E+0 1.00E+08 1.00E+09

Cycles to Failure

Fatigue

Streng

th-

psi


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Estimating Se or Sf

For ____________:

Se = .

Sut for

Sut< ksi ( MPa)Se = ksi (7 MPa)

forSut> ksi ( MPa)

For ______________:

Se = . Sut forSut6 ksi ( MPa)


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Estimating Se or Sf contd

For __________________:

Sf@ E8 = .

Sut for

Sut ksi ( MPa)

For _____________________:

Se = . Sut forSut< ksi ( 80 MPa)

Se = ksi ( 00 MPa)

forSut> 0 ksi ( 80 MPa)


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Correction Factors to EnduranceLimit and Fatigue Strength

Se = load size surf temp reliab Se

Sf= load size surf temp reliab Sf

Se - corrected endurance limit for a part

Sf- corrected fatigue strength for a part


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Cload - load factor see eq. 6.7a pg 8

Csize - size factor see eqs. 6.7a,b,c

pg 8-

Csurf- surface factor see Figs. 6- 6,6. 7, and eq. 6.7e pg -


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Ctemp - temperature factor see eq. 6.7f

pg - Creliab - reliability factor see Table 6.

pg


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Stress Concentration Kf= q(Kt+ )

Kt- geometric stress concentrationfactor

Kf-___________________________

q - notch sensitivity factor


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Fluctuati

ng Stresses

Modified-Goodman Diagram


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Failure Lines for Fluctuating Stress


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Augmented Modified-Goodman

Diagram


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Stress Concentration

Apply Kfto the ______________

components of stress. For __________ materials apply Kt to

the mean components of stress.


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Factor of Safety for Fluctuating Stress -

Case 1


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Case 2


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Case 3


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Case 3


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Case 4


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Case 4


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Fluc

tuatin

g Stresses

Multiaxial Stresses in Fatigue


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Fully Reversed SimpleMultiaxial Stresses


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Fluctuating Simple Multiaxial Stresses

Von Mises Method


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General Approach to High Cycle

Fatigue Design Generate Modified Goodman Diagram

Calculate alternating and mean components

of stress at areas of concern on the part.Include appropriate stress concentrationfactors.

Convert alternating and mean appliedstresses to alternating and mean Von Mises

Stresses. Plot these stresses on the Modified Goodman

Diagram and find the factor of safety.


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Example The figure pertains to the shaft of a disk

sander that is made from steel havingSu= 00 MPa, and Sy=7 0 MPa. The most

severe loading occurs when an object is heldnear the periphery of the disk with sufficientforce to develop N-m (which approachesthe stall torque of the motor).

Assume a coefficient of friction between theobject and the disk is 0.6.

What is the factor of safety with respect toeventual fatigue failure of the shaft?


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Example

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Lec 3 Fatigue Failure 031004_for_students